Jacobian math homework

  • Thread starter phrygian
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  • #1
phrygian
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Homework Statement



Suppose that P, Q, and R are regions in R2, and suppose T1 : P -> Q and T2 : Q -> R are
dierentiable. Use the (multivariable) Chain Rule and det(AB) = det(A)det(B) to show that the Jacobian of the
composition T2 o T1 is the product of the Jacobians of T1 and T2.


Homework Equations





The Attempt at a Solution



So if I say T1 is given by x = g(u,v) and y = h(u,v) and T2 is given by u = i(s,t) and v = j(s,t) , I know how to find the two jacobians T1 and T2 but am confused how do you find the jacobian of the composite transformation T1 o T2?
 

Answers and Replies

  • #2
ystael
352
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Follow their instructions: use the chain rule to compute the derivative of [tex]T_2 \circ T_1[/tex].
 

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